926
TEDB, FLANAGAN AND CHANQ HWANKIM
siderably !mailer than the diameter of the rubidium ion, 2.96 A., but larger than the 1.90 A. of the K a + ion. It thus seem8 that ions smaller than potassium are too small to coordinate effectively with the
Vol. 66
hydrogen peroxide molecule; however, the larger charge densities of the smaller ions lead to very effective coardination with the smaller water molecule.
THE EFFECT OF IRRADIATIOS UPOS THE KINETICS OF AS ENDOTHERMIC SOLID REACTIOS. THE DEHYDRATIOS OF hllAKGASOUS OXALATE DIHYDRATE1 B Y TEDB.
FLhNAGAN’ AND CHAICG H ~ A E N( I M ~
Brookhaven iyational Laboratory, Upton, L. I.,
New Yorlc
Receired December 20, 1961
The kinetics of dehydration of virgin and reactor-irradiated manganous oxalate dihydrate have been examined with the aid of a quartz helix balance. The maximum rate of dehydration was noted to increase by a factor of approximately 3 times (70’) while the activation energy was reduced from 22.3 0.7 to 17.3 =t0.7 kcal./mole after a total neutron dose of 6.05 X 1018 n. cm.?.
Introduction The dehydration of niaiiganous oxalate dihydrate has been studied by Topley and Smith4 and Volmer and Seyde1.j Indeed manganous oxalate dihydrate is of some historic interest because the “Topley-Smith effect,” i.e., an unusual dependence of the rate of dehydration upon the surrounding water vapor pressure, first was observed with this compound (e.g., see ref. 6). Topley and Smith found an activation energy of 24.3 kca1.l mole for the dehydration; their rate constants mere determined somewhat arbitrarily, as the rate of loss of water vapor per decigram of manganous oxalate dihydrate at 20% dehydration. While there have been many recent studies of the effects of irradiation, e . g . , p r a y and neutron, upon exothermic solid decompositions, (see especially ref. 7 to 11), there has been a lack of‘ such studies for endothermic r e a c t i o i i ~ . Manganous ~~~~~ oxalate dihydrate was chosen since the dehydration of virgin material had been investigated previously and because the subsequent thermal decomposition of the anhydride also could be investigated.14 Experimental Materials.-Nanganous oxalate dihydrate 1%as prepared by the addition of potassium permanganate to a stirred oxalic acid solution at 8Oo1j and also by addition of manga(1) Work performed under the auspices of the E. S. Atomic Energy Commission. ( 2 ) T o whom inquiries should be sent regarding this work; present address: Chemistry Department, University of Vermont, Burlington, Vermont. (3) Participant summer student program, Brookhaven National Laboratory. ( 4 ) B. Topley and M.L. Smith, J . Chem. Soc., 321 (1935). ( 5 ) M. Volmer and G. Seydel, 2. physilc. Chem., A179, 153 (1937). ( 6 ) W. E. Garner, in “Chemistry of the Solid State,” ed. Garner, Butterworths, London, 1955, Chap. 8. (7) E. G. Prout, J . Inorg. R. Nuclear Chern., 7 , 368 11958). (8) E. G. Prout a n d M. J. Sole, ibid., 9, 232 (1959). (9) P J. Herley and E. G. Prout, ibid., 16, 16 (1960). (10) E. G. Prout, LVature,183,884 (1959). (11) P. J. Herley and E. G. Prout, J . Chem. SOC.,3300 (1959). (12) T. B. Flanagan, Trans. Faraday Sac., 55, 114 (1959). (13) P. J. Herley and E. G. Prout, J . Am. Chcm. Soc., 82, 1540 (1960). (14) T. B. Flanagan, to be published. (1.5) R. W. Coltman, l a d . Eny. Chsm., 16, 606 (1924).
nous carbonate to a hot, stirred oxalic acid solution. Microscopic examination revealed that the dihydrate resulting from both preparations was predominately in the form of rhombohedral plates; in addition, however, some long, prismatic crystals were noted. Several preparations using the manganous carbonate and oxalic acid procedure failed to eliminate the long prisms completely.15 Finally a preparation with a great majority of crystals in the rhombohedral platelet form was employed for the dehydration studies. It was observed, however, that there was negligible difference between the dehydration-time curves of material from the two preparative procedures. The particle size was less than 5 p . Elemental analysis gave: C = 13.42% and H = 2.21% compared to the theoretical values of C = 13.4170 and H = 2.257. for the dihydrate. Apparatus.-The dehydration was studied with the aid of a quartz helix balance (sensitivity 1 crn./l mg., Microchemical Specialties, Berkeley, California). One to 2mg. samples were employed. In the study of endothermic solid state reactions self-cooling often is present16 and consequently the temperature of the sample may be lower than that measured in the furnace. Self-cooling corrections can be made if the sample’s area is known accurately, i . e . , if large single crystals are employed.16 To eliminate selfcooling when employing fine particles, hydrogen gas may be added to the reaction vessel to aid in heat transfer to the sample during dehydration. Topley and Smith4 used this procedure. Helium gas was employed in the present investigation and it was observed that the rate was sensitive to small variations in the helium pressure. The effect of the helium pressure on the rate of dehydration a t both 85 and 95” was investigated. In both cases a maximum in the rate of dehydration occurred at approximately 0.15 mm. of helium; hence, this pressure was employed for determination of the activation energy. -4 self-cooling curve also was determined for an irradiated sample (6.05 X 1018 n. it was found that self-cooling was also of importance in this case, but the rate was not so sensitive to the helium pressure (70”)as was the rate of virgin samples. d pressure of 0.15 mm. of helium also was chosen for the determination of the activation energy of the irradiated sample. Irradiation Procedure.-Small samples, 10 to 40 mg., were placed in quartz containers ( 5 cc.) and evacuated to approximately 10-8 mm. before sealing off in vacuo. The samples then were irradiated in a water-cooled “hole” of the Brookhaven graphite research reactor. In the absence of any appreciable radiation heating due to the presence of a large sample or sample container, the measured temperature of the “hole” is 40 to 50’. The sample vessels were equipped with a break-off seal and could be opened into the high vacuum system to determine the gas evolved after irradiation. One sample was irradiated in air. This (16) M. L. Smith and B. Topley, Proc. Ray. Soc. (London), 8134, 224 (1931).
May, 1962
KINETICS OF
AN
ENDOTHERMIC SOLIDREACTION
Sam le waz wrapped with aluminum foil and placed in a smaf alummum container. Several of the ssinplea were weighed before and after irradiation. The tots1 neutron flux in the reactor “hole” employed was -loo X 1018 n , cm.-2 aeo.-1. The fast neutron flux (>0.4 Mev.) was 4.6 X 1011 n. cm.-zset.-' and the approximate ?-flux wa.~2.7 X lo8r,/hr,
Results Dehydration of Virgin Samples.--A typical dehydration run is shown in Fig. l (70”, 0.15 mm. of helium). The shape of the dehydration curve is typical of dehydration reactions which have not been artificially nucleated.6 The time sequence of phases in the per cent. dehydration-time curve is as follows: phase (a) an induction period, phase (b) a slow reaction period, phase (e) a constant reaction rate, and finally phase (d) a deceleratory phase (Fig. 1). I n a typical run, such as shown in Fig. 1, only 90 to 95% of the two molecules of mater were lost from the oxalate at temperatures from 55 to 95’. After heating in an air furnace a t 110’ for 30 hr,, 97% of the watcr was lost. Heating in VUCZLO a t 150’ removes approximately 100% of the water. Apparently the last 5% of the mater of hydration is comparatively {difficultto remove; this behavior was noted to an even greater degree in irradiated samples (see below). Garner and others6 have studied many dehydration reactions and have established that the majority of these reactions proceed in the following way: nuclei formation on the surface (this usually is preceded by an induction period), coalescence of these nuclei to establish an interface, and growth of the interface into the volume of the crystal. The events observed in the a-time curve (Fig. l ) , a = percentage dehydration, can be tentatively interpreted in terms of the mechanism outlined above : phase (a) represents preiiucleatioii phenomena, phase (b) nuclei formation and coalescence, phase (c) penetration into thc interior by a constant area interface, which was established during phase (b), and phase (d) represents deceleration of the rcactioii, probably in part due to complete reaction of the smaller crystals. Microscopic observations confirmed this general picture of the dehydration process. With the aid of time-lapse photography, the dehydration process could be followed directly on a vacuum heating stage. These studies revealed that nuclei formed on the surface of’ the rhombohedral plates; the nuclei appeared to form preferentially at ridges and imperiections on the surface and not necessarily a t the edges or corners. The nuclei then grew and coalesced. The plates became relatively opaque after dehydration as compared to the virgin samples. No change in the external shape of the crystals occurred flollowing dehydration. It mas noted from Fig. 1 that a linear rate extends from 10 to 40% dehydration; these percentages are independent of temperature. The distribution of sizes among the crystals precluded a detailed “curve fitting” to the entire dehydration curve. Rate constants were calculated from the slope of the linear portion of the dehydration curve. Rate constants calculated in this manner correspond t o penetration into the
927
80
U I
z
0
c a a n
60
>-
I W
n
c 40
z
W
u a W
a 20
0
50
I50
100
TIME(IN MINUTES).
Fig. 1,-The dehydration of manganous oxalate dihydrate (70°, 0.15 mm. helium): A, virgin sample; 0 , reactor-irradiated sample (6.0 X 10‘8 n. cm.-2); 0, sample dehydrated and rehydrated prior to the dehydration shown in this figure.
6 5
2 70
2 00
2 90
300
310
320
I I T x 10:
Fig. 2.-The Arrheniua plot for the dehydration of manganous oxalate dihydrate (0.15 Inm. helium): c), virgin sample; 0 , reactor-irradiated sample (6.0 X 1018 n. cm.-2).
crystals by an interface of constant area judging from both microscopic observations and by
T ~ B. D FLANAGAN AND CHANG HWANKIM
928
c 4
J
L 0
20
40
60 80 T I M E (MINUTES).
100
I20
Fig. 3.-The effect of reactor-irradiation upon the dehydration of manganous oxalate dihydrate (75", 0.15 mm. helium): V, virgin sample; A, 2.2 x 1018 n. cm.-2; B, 4.6 X 1018n.crn.-2; C, 5.2 X 101*n.cm.-*; D, 6.0 X 10'8n. cm.-* (irradiated in air); E, 9.8 X 10'8 n. cm.-2.
analogy with other dehydration reactions. Figure 2 shows the Arrhenius plot of these rate constants; the activation energy is 22.3 i 0.7 kcal./mole. Self-cooling in vacuo was negligible below 5 5 O . The linearity of the Arrhenius plot (Fig. 2 ) attests to the successful elimination of self-cooling. The induction time also follows the Arrhenius relation with an activation energy of 24.1 i 1.2 kcal./ mole. The value of 22.3 kcal./mole is somewhat smaller than the value of 24.3 kcal./mole found by Topley and Smith.4 Dehydration of Reactor-Irradiated Samples.Figure 1 shows the comparison of the dehydration curve of a virgin and a reactor-irradiated sample (6.05 X lo1*n. It is noted that irradiation greatly affects the kinetics of dehydration; for example, in Fig. 1 the induction time has been decreased from 28 to 6 min. The subsequent linear rate of dehydration in the irradiated sample extends from a = 0 to a = 40% dehydration. The magnitude of the linear rate constant for dehydration of the irradiated sample is 3.2 times as great as that of the unirradiated sample (70'). It should be noted that although the rates have been enhanced the general shape of the dehydration curve has not been markedly altered after irradiation (Fig. 1). Microscopic examination of the irradiated samples during their dehydration revealed no pronounced differences from the behavior of unirradiated samples, e.g., there was no cracking or crumbling of the irradiated samples. Figure 3 shows the effect of total neutron irradiation dose upon the percentage dehydration-time curves (75', 0.15 mm. of helium). All but one of the samples were irradiated in vacuo17; the exception, sample D, was irradiated in the atmosphere of the reactor. (The samples henceforth will be referred to as they are labeled in Fig. 3.) It is noted from Fig. 3 that the dehydra(17) The samples were sealod into quartz containers a t 10" mm. pressure b u t radiation-induced deoomposition of oxalate ions caused the pressure t o increase during irradiation, e.@., the pressure over sample C was -5 mm. (COSand CO) after irradiation.
Vol. 66
tion behavior of the sample irradiated in the atmosphere of the reactor does not differ markedly from a sample irradiated in vacuo a t a slightly smaller total neutron dose (sample C). A plot of the rate of dehydration vs. total neutron dose is quite linear over the range studied, &e., to 9.8 X lo1* n. em.+ (75', 0.15 mm. He). The sample irradiated in air ialls on the straight line. An additional difference between the dehydration behavior of irradiated and virgin samples is that the amount of water lost after several hours of dehydration a t 75' decreases somewhat after irradiation. For example, sample D looses approximately 75% of its water after 48 hr. of heating in vacuo a t 75'. Upon heating to 150' the remainder of the water is lost rapidly. It is expected that samples A through D still retain 100% of their water after irradiation since there was no indication of any water vapor upon opening these samples into the vacuum system. Sample E, however, did evolve some water vapor upon opening the container. Prolonged heating of sample E in vacuo a t 135' showed that only 94% of the two moles of water were retained after irradiation. If decomposition occurs a t 135' or lower temperatures, the dehydration data will of course be erroneous. This seems unlikely since observable decomposition of unirradiated samples does not occur readily until the temperature is raised to approximately 300" and irradiation does not increase the rate of decompo~ition.~~ That decomposition is not a factor was shown more conclusively by the following experiment: Sample E was dehydrated in a closed vacuum system while the water vapor was condensed into a liquid nitrogen trap. After several hours heating a t 135O, pressure readings still indicated a good vacuum. Since CO is one of the decomposition product^,'^ any decomposition would be indicated by an increase of pressure. Additional evidence against decomposition occurring was the visual absence of decomposition, i.e., the sample still was whitish in appearance while the decomposition residue was dark.14 Evidence that Samples Were Not Dehydrated during Irradiation.-In order for the kinetic data of the irradiated samples to be meaningful the samples must not have been dehydrated during irradiation, either thermally or as a direct result of irradiation, and then rehydrated after removal from the reactor. The following evidence will be cited to strongly suggest that the samples were not dehydrated during irradiation. (1) While dehydration of irradiated samples was appreciable a t 40 to 50' in vacuo (Fig. 2), dehydration of an irradiated sample (D) did not occur in the laboratory atmosphere after 120 hr. a t 60'. On the basis of this evidence, sample D would not have been dehydrated during its irradiation in air (40-50') and since its kinetic behavior resembles samples irradiated with a comparable dose in, vacuo (Fig. 3), it is probable that these latter samples were not dehydrated during irradiation. ( 2 ) The rate of rehydration of the anhydride to the dihydrate was extremely slow under conditions
May, 1962
KINETICS OF AN ENDOTHERMIC SOLID REACTION
more favorable for rehydration than the irradiated samples were subjected to. (3) The absence of either water vapor or significant weight loss was noted after opening samples A t o D. (4)The magnitude of the rate of dehydration of a rehydrated sample (unirradiated) was closer to that of the virgin than that of an irradiated sample (Fig. 1). (5) Microscopic examination revealed that rehydrated samples appeared more opaque than either irradiated or virgin samples. There is, however, an incongruity in the evidence; namely, the dehydration of an irradiated sample is appreciable a t 4 5 O in vacuo (Fig. 2), but dehydration of the sarnples sealed into quartz ampoules in vacuo apparently did not occur after many hours of irradiation. The most likely explanation of this is that the samples which were sealed into quartz ampoules were not in fact irradiated zn vacuo because of the occurrence of radiation-induced decomposition of oxalate ions. While the percentage decomposition was small, the small size of the sample containers allowed appreciable pressures of gas to accumulate (mainly C O ) , e.g., for sample C approximately 5 mm. of gas was present in the ampoule after irradiation. It is suggested that thle presence of this gas successfully inhibited the dehydration reaction. Dehydration of y-Irradiated Sample.-A sample was irradiated as the dihydrate in vacuo a t room temperature for a total dose of 1.6 X lo8r. (GOao). The dehydration characteristics of this sample were studied. It was found that the subsequent dehydration curve was unaffected by this dose of y-rays. Activation Energies for Dehydration of Irradiated Samples.-The Anhenius plot of the activation energy for dehydration of a reactor-irradiated sample (6.05 X 10'8 n. irradiated in air) is shown in Fig. 2 in comparison with a virgin sample. The activation energy has been reduced by irradiation from 22.3 f 0.7 to 17.3 0.7 kcal./mole. This means that there must be a compensating reduction in the pre-exponential factor for dehydration of irradiated samples because the decrease in the activation energy is too large to account for the observed increase in rate. The activation energy for the induction period is also 17 kcal./mole (this should be regarded as an approximate value) ; it is, however, significantly lower than the value of 24 kcal./mole found for virgin samples.
*
Discussion As has been pointed out above, the shape of the per cent. dehydration-time curve for the dehydration of virgin manganous oxalate dihydrate (e.g., Fig. 1) is to be expected for a contracting envelope mechanism when the particles have not been artificially nucleated.6 The linear rate extends over a significant fraction of the dehydration curve because nucleation and growth are confined to the two large surfaces of the rhombohedral plates. The activation energy calculated from the induction time is larger than that obtained from the linear rate constants. This suggests that the activation energy for nucleation is greater than that for
929
nuclei growth (interfacial penetration) ; this is reasonable.6 The following discussion pertains t o the irradiated sample most completely investigated, that is, sample D (total neutron dose of 6.05 X 10" n. cm.-2) (see Fig. 1 and 3). In virgin samples the early non-linear region, phase (b), usually extends from 0 to 10% dehydration; in the irradiated sample shown in Fig, 1 the linear region commeiices from almost the start of the dehydration. This implies that nucleation and the establishment of the constant area interface must occur simultaneously. Reactor irradiation introduces many potential nucleation sites which will be homogeneously distributed throughout the crystals. The damaged regions on the surface of the plates rapidly nucleate and coalesce upon heating. The resulting interface penetrates into crystals as for unirradiated samples, but the rate of penetration into the irradiated matrix will be enhanced due to the presence of internal radiation damage. The final deviations from linearity occur near 40% dehydration; this is comparable to the point of deviation in unirradiated samples and is consistent with the fact that essentially the same mechanism of dehydration occurs in irradiated and virgin samples. Damaged regions in the lattice may arise from decomposition of oxalate ions by ionizing radiation or by atomic displacements resulting from either fast neutron knock-on collisions or recoil of manganese atoms from the h/In56(n,r) MnS8reaction. Walker1*has estimated that slow neutron capture by manganese will cause approximately l/z of the total atomic displacements in pure manganese. It is believed that ionizing radiation, which decomposes isolated oxalate ions, does not contribute significantly to the increase in the rate of dehydration, because isolated defects would not affect the progression of the interface as markedly as regions of damage extending over several hundred molecules (resulting from displacement or thermal spikes). I n support of this a 7-ray dose close to that obtained during the reactor irradiation of sample A (Fig. 3) did not affect the subsequent dehydration. The majority of the damage will arise from fast neutron knock-on collisions onto C, H, 0, and Mn. There also will be a significant contribution by the recoil damage caused by Mn56. The effects of nuclear irradiation upon the subsequent exothermic decomposition of solids have been studied by a number of workers.7-11P-22 In most cases sample irradiation increases the rate of decomposition and decreases the induction period (if an induction period is present before irradiation). I n exothermic decomposition reactions radiation may alter the mechanism of decomposition.22 The possibility of a change in the mechanism of an endothermic dehydration reac(18) R. M. Walker, J . Nuclear Materials, 2, 147 (1960). (19) T. B. Flanagan. Nature, 181, 42 (1958); J . Phgs. Chem., 66, 416 (1962). (20) J. Jaah, "Proo. Int. Symp. on Reactivity Solids,'' Amsterdam, 1960. (21) J. M. Groocoak, Proc. Roy. SOC.(London), 2468, 225 (1958). (22) R. M. Haynes and D. A. Young, Discussions Faraday SOC.,31, 220 (1961).
930
ROBERT W. KUNZE AND RAYMOND M, Fuoss
tion after irradiation is less likely, since the simple contracting envelope mechanism invariably observed for dehydration reactions6 is not likely t o be significantly altered by radiation unless macrodisruption of the crystals occurs. Hence the evaluation of radiation damage as reflected by the subsequent decomposition kinetics would be expected to be more unequivocal in endothermic systems. Both dehydration reactions studied to date,l2 (this investigation) have required comparatively large doses of reactor-irradiationlo for their sub-
Yol, 66
sequent dehydration-time curves to be affected. I n addition Herley and Proutla found that the decomposition of silver oxide mas unaffected after an exposure of 1.8 X 1017n. (fast). Judging from these results endothermic solid state decomposition reactions are less affected by irradiation than are exothermic reactions. Acknowledgments.-Dr. G. J. Dienes is thanked for his encouragement and advice. The cooperation of the Picatinny Arsenal Explosives Research group a t Brookhaven National Laboratory is gratefully acknowledged.
CONDUCTANCE OF THE ALKALI HALIDES. 111. THE ISOTOPIC LITHIUM CHLORIDES1 BY ROBERTW. KUXZE AND RAYMOND M. Fuoss Contribution No. 1687 f r o m the Sterling Chemistry Laboratory of Yale University, Xew Haven, Connecticut Receibed December 86, 1061
The conductances of the chlorides of Li* and Li7in water a t 25” have been measured over the concentration range 0.002) 0.01 A‘. The limiting conductances are ho(Li6C1)= 115.23 and A . o ( L ~ ~=C ~115.10. The difference of 0.13 (6 times experimental error) corresponds to a 0.35y0greater mobility for the ion of Lio.
Yatural lithium consists predominantly (92.02%) of the heavier isotope; present availability of each isotope in a state of high purity suggested a comparison of their conductances in order to verify the expected existence of a small difference in mobility. It has been shown that a small isotope effect exists for lithium nitrate dissolved in sodium-potassium nitrate e~tectic,2-~ although considerably smaller than the difference in masses (0.089 vs. 1/7). Arnikar recently4 reported a relative mobility difference Av/v = 0.0036, based on measurements of migration of lithium chloride in agar gel. The purpose of this paper is to present the results of a series of measurements of the conductance of the chlorides of Li6and Li7in water a t 25’. We find AXa/ho(Li+) = 0.0035, in complete agreement with hrnikar’s result. Experimental Materials.--The lithium chloride was used as received from the Isoto es Division of the Oak Ridge National Laboratory. eT ! isotopic compositions reported for the samples were L i T I (95.62% LP) and L i U (99.9926% Li7). According to spectrographic analysis, other cations were present a t most in only trace amounts, less than O.Ol%, except the Li6Cl, for which 0.1% calcium was reported. Assuming the calcium present as chloride, the error due to replacing LiCl by an equal weight of CaClz is nearly compensated by the higher equivalent conductance of Ca?. Distilled water with a specific conductance of about was used; the conductance was measured in the cell before adding the first portion of lithium chloride. Our lowest soIution conductances were of the order of 200 X 10-8; since the solvent conductance was known to 1-2%, the maximum uncertainty from this source was about 0.01% in solute conductance. (1) Results presented in this paper will be included in a thesis t o be presented by Robert W. Kunze to the Graduate School of Yale University in partial fulfillment of the requirements for the degree of Doctor of Philosophy. ( 2 ) M. Chemla, Compt. rend., 242, 1150 (1956). (3) H. J. Arnikar and M. Chemla, J . A p p l . Rad. Isotopes, 2, 261 (1957). (41 E. J. Arnikar, J . Inorg. & Nuclear Chem., 10, 248 (1959).
Methods.-Lithium chloride was dissolved in water t o give approximately 0.1 N solution; a portion of about 1520 g. of this solution was weighed from a weight buret into the water in the conductance cell to give a starting solution of about 0.01 N in the cell. Further points were obtained by adding successive portions of water to the cell. All concentrations thus were determined by weight (and corrected to vacuum); they were computed to volume concentrations c (eq./l.) by the equation5 c / m = 0.99707 0.0182m. The concentrations of the master solutions were determined by differential potentiometric titration6 of 40-50-g. samples against 0.1 Ar silver nitrate solution. The titration was carried almost to the end-point using silver nitrate solution from a weight buret; then the final part of the titration was made using 0.004 N silver nitrate solution from a volumetric buret. All titrations were made near 0” in order to sharpen the end-point (about 10 mv. break). The silver nitrate solutions were standardized by using them to titrate portions of our purified potassium chloride7; about 400-mg. portions of the latter were weighed on the microbalance. I n all, three master solutions (a, b, c) of LieCl and two (d, e) of LiT1 were prepared; the corresponding conductance data are indicated by the superscripts on the run numbers in Tables I and 11. All standardizations (both of lithium chloride solutions and of the silver nitrate solutions prepared individually for each master solution) are based on (at least) triplicate analyses; the standard deviation over the 12 silver nitrate-potassium chloride titrations was 0.01470, and over the 21 lithium chloride-silver nitrate titrations was 0.00770. 4 s a check on the method, a master solution of sodium chloride, purified for conductance, was prepared and analyzed; it then was used in a conductance run by the dilution technique used for lithium chloride; the points so obtained ( c = 0.0049266, A = 120.650; c = 0.0030570, A = 121.796) agree within 0.01 A-unit with the average of literature values.8-10 The conductance cell used for all the measurements had a constant of 1.01090 i 0.00024, based on 21 determinations (5) H. S. Harned and B. B. Owen, “The Physical Chemistry of Electrolytic Solutions,” Reinhold Publ. Corp., New York, N. Y . , third edition, 1958, p. 716. (6) N. F. Hall, M. A. Jensen, and S. A. Baeckstrom, J . A m . Chem. Soc., 60, 2217 (1928). (7) J. E. Lind, Jr., and R. M. Fuoss, J . Phys. Chem., 66, 990 (1061). (8) T. Shedlovsky, J . Am. Chem. Soc., 54, 1411 (1932). (9) G. C. Benson and A. R. Gordon, J . Chem. Phys., 13,473 (1945). (10) F. W. Tober, dissertation, Yale University, 1948.
